A single-tooth twin-screw rotor with low transmission requirements and its profile design method

Abstract

The present invention discloses a single-tooth twin-screw rotor with low transmission requirements and a profile design method thereof. The single-tooth twin-screw rotor comprises a low gas torque rotor and a high gas torque rotor meshing with each other. The profiles of the low gas torque rotor and the high gas torque rotor are formed by connecting a combined curve segment generated by a rack curve and a point-meshing cycloid segment; the rack curve A r B r C r D r E r From the straight line segment A r B r , Bezier curve segment B r C r , Bezier curve segment C r D r With straight line segment D r E r The combined curve segments of the low-gas-torque rotor profile and the high-gas-torque rotor profile mesh with the rack curve. The combined curve segments connect their respective meshing cycloid segments, resulting in a complete rotor profile structure for both the low-gas-torque rotor and the high-gas-torque rotor. This invention reduces the required torque transmission between the male and female rotors, effectively alleviating rotor wear.

Description

Technical Field

[0001] The present invention belongs to the technical field of twin-screw machinery, and in particular relates to a single-tooth twin-screw rotor with low transmission requirements and a profile design method thereof. Background Art

[0002] Twin-screw extruders are positive displacement rotary machines with forced suction and exhaust functions. They are widely used in modern industry as compressors, expanders, and vacuum pumps. Compared to other positive displacement machines, they offer advantages such as reliable operation, low cost, no wearing parts such as air valves, compatibility with liquids, and high efficiency.

[0003] The core component of a twin-screw extruder is a pair of intermeshing rotors. The rotor profile is a key design element, and its design directly determines the overall thermodynamic performance of the machine. Traditional twin-screw extruders feature a multi-tooth rotor profile, which relies on the meshing of the male and female rotor profiles to achieve periodic intake and exhaust. In typical liquid injection screw extruders, this meshing motion relies on the male rotor as the motor drive shaft, which then transmits gas torque to the female rotor through contact meshing. To reduce contact force between the male and female rotors, a multi-tooth profile can be designed to minimize the gas resistance torque on the female rotor. Single-tooth rotor profiles are widely used in dry screw vacuum pumps, offering high sealing performance and high volume utilization. However, when used in liquid injection applications, the identical profiles of the male and female rotors result in an even distribution of gas resistance torque between the two rotors. This results in a higher gas torque being transmitted by the male and female rotors. Furthermore, the meshing curve length of the single-tooth profile is relatively low, making rotor wear more likely. Summary of the Invention

[0004] The purpose of the present invention is to address the problems in the above-mentioned prior art and provide a single-tooth twin-screw rotor with low transmission requirements and a design method for its profile, thereby reducing the transmission torque required between the male and female rotors and promoting the application of the single-tooth profile in liquid spraying conditions.

[0005] In order to achieve the above object, the present invention has the following technical solutions:

[0006] A single-tooth twin-screw rotor with low transmission requirements, comprising a low gas torque rotor and a high gas torque rotor meshing with each other, wherein the profiles of the low gas torque rotor and the high gas torque rotor are both formed by a rack curve A. r B r C r D r E r The generated combined curve segment is connected with the point meshing cycloid segment; the rack curve A r B r C r D r E r From the straight line segment Ar B r , Bezier curve segment B r C r , Bezier curve segment C r D r With straight line segment D r E r The combined curve segments A1B1C1D1E1 of the low gas torque rotor profile and A2B2C2D2E2 of the high gas torque rotor profile are connected to the rack curve A r B r C r D r E r The meshing relationship is satisfied, and the combined curve segment A1B1C1D1E1 and the combined curve segment A2B2C2D2E2 are respectively connected to the point-meshing cycloid segment E1A1 and the point-meshing cycloid segment E2A2 to obtain the complete rotor profile structure of the low gas torque rotor and the high gas torque rotor.

[0007] As a preferred solution, in coordinate system O r x r y r In the example, the straight line segment A r B r The parametric equations are as follows:

[0008]

[0009] Where x AB with y AB Represents the straight line segment A r B r The horizontal and vertical coordinates of the rack curve A are shown in Figure 2. r B r C r D r E r The parameter, R p is the pitch circle radius, R p equal R1 and R2 represent the set root circle radius and tooth tip circle radius respectively, γ1 is point B r Position setting parameters.

[0010] As a preferred solution, the Bezier curve segment B r C r The position vector expression of the upper point is:

[0011]

[0012] Where r BC Represents the position vector of the point on the Bezier curve segment BC, r B With rC Represents point B r and point C r The position vector, r P1,AB With r P2,AB Represents point P respectively 1,AB and point P 2,AB The position vector of

[0013] Click P 1,AB and point P 2,AB Select line segment B r P 0,AB With line segment C r P 0,AB For a point on , the direction vector expression is:

[0014]

[0015] Where i 1,AB with i 2,AB Point P 1,AB and point P 2,AB The location parameter is the design parameter, r P0 Represents point P 0,AB Position vector of point P 0,AB Line B r P 0,AB With straight line C r P 0,AB The intersection of straight line B r P 0,AB With Oy r Axis parallel, straight line C r P 0,AB Passing point C r , point C r Via Oy r Axis, the slope is from point C r Determined by the direction vector at point C r The direction vector at is determined by the design angle β;

[0016] Point C r The position vector is:

[0017] r C =[0 δR p ]

[0018] Where δ is point C r The control variable is the design value;

[0019] Point B r The position vector is:

[0020] r B =[R p -R2 πR p-γR p ].

[0021] As a preferred solution, the Bezier curve segment C r D r The position vector expression of the upper point is:

[0022]

[0023] Where r CD Represents Bezier curve segment C r D r The position vector of the upper point, r C With r D Represents point C r and point D r The position vector, r P1,CD With r P2,CD Represents point P respectively 1,CD and point P 2,CD The position vector of

[0024] Click P 1,CD and point P 2,CD Select line segment C respectively r P 0,CD With line segment D r P 0,CD For a point on , the direction vector expression is:

[0025]

[0026] Where i 1,CD with i 2,CD Point P 1,CD and point P 2,CD The location parameter is the design parameter, r P0,CD Represents point P 0,CD Position vector of point P 0,CD is the straight line C r P 0,CD With straight line D r P 0,CD The intersection of the straight line D r P 0,CD With Oy r Axis parallel, straight line C r P 0,CD With straight line C r P 0,AB parallel;

[0027] Point D r The position vector is:

[0028] r D =[R2-R p γ2Rp ]

[0029] Where γ2 is point D r The control variable is the design value.

[0030] As a preferred solution, the straight line segment D r E r Point E r The position vector is:

[0031] r E =[R2-R p -πR p ].

[0032] As a preferred solution, in the rectangular coordinate system O1x1y1, the profile expression of the combined curve segment A1B1C1D1E1 is as follows:

[0033]

[0034] In the rectangular coordinate system O2x2y2, the profile expression of the combined curve segment A2B2C2D2E2 is as follows:

[0035]

[0036] Where r A1B1C1D1E1 Represents the position vector of a point on the combined curve segment A1B1C1D1E1 in the rectangular coordinate system O1x1y1, r A2B2C2D2E2 Represents the position vector of a point on the combined curve segment A2B2C2D2E2 in the rectangular coordinate system O2x2y2, r AE with y r AE Respectively expressed in coordinate system Ox r y r Middle rack curve A r B r C r D r E r The horizontal and vertical coordinate vectors of the upper point, t represents the rack curve A r B r C r D r E r The parameter variable, φ represents the intermediate angle variable parameter, and the relationship between φ and t is:

[0037]

[0038] As a preferred solution, the profile expressions of the point-meshing cycloid segment E1A1 and the point-meshing cycloid segment E2A2 are:

[0039]

[0040] Where x AE with y AE They respectively represent the coordinate vectors of the midpoint meshing cycloid segment E1A1 of the coordinate system O1x1y1 or the midpoint meshing cycloid segment E2A2 of the coordinate system O2x2y2.

[0041] A method for designing a profile of a single-tooth twin-screw rotor with low transmission requirements comprises the following steps:

[0042] Step 1: Design rack curve A r B r C r D r E r :

[0043] The rotor tooth root circle radius R1 and tooth tip circle radius R2 are set according to the exhaust volume requirement;

[0044] Set point B according to sealing requirements r Position setting parameter γ1, control point D r The setting parameter γ2 of the position;

[0045] Design point C according to the rotor gas torque adjustment requirement r The control variable δ of the position;

[0046] Based on point C r The direction vector at determines the design angle β and sets the Bezier curve segment B r C r The shape control parameter i 1,AB with i 2,AB , set Bezier curve segment C r D r The shape control parameter i 1,CD with i 2,CD ;

[0047] Step 2: According to the meshing theorem, the rack curve A designed in step 1 r B r C r D r E r Calculate the combined curve segment A1B1C1D1E1 of the low gas torque rotor profile and the combined curve segment A2B2C2D2E2 of the high gas torque rotor profile;

[0048] Step 3, solve the point meshing cycloid segment E1A1 and the point meshing cycloid segment E2A2;

[0049] Step 4: Connect the combined curve segment A1B1C1D1E1 with the point-meshing cycloid segment E1A1 to form a low gas torque rotor profile; connect the combined curve segment A2B2C2D2E2 with the point-meshing cycloid segment E2A2 to form a high gas torque rotor profile.

[0050] As a preferred solution, the low gas torque rotor profile and the high gas torque rotor profile are formed into a constant pitch or variable pitch screw rotor structure through lofting.

[0051] Compared with the prior art, the present invention has at least the following beneficial effects:

[0052] A rack curve of a single-tooth rotor profile is formed by using straight line segments and Bezier curve segments, and then a combined curve segment of the single-tooth profile is solved according to the meshing relationship. By connecting the combined curve segment with the point-meshing cycloid segment, a complete yin-yang rotor profile can be formed. The required transmission torque between the yin-yang rotors can be adjusted by adjusting the profile parameters. The low-gas-torque rotor profile and the high-gas-torque rotor profile designed by the present invention can achieve correct meshing, and the flexible adjustment of the rotor profile shape can be achieved by adjusting the design parameters of the profile generation process. The screw rotor generated by the profile structure of the present invention, when applied to liquid spraying conditions, can reduce the required transmission torque between the yin-yang rotors and effectively alleviate rotor wear. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Rotor rack curve A in the embodiment of the present invention r B r C r D r E r Structural diagram;

[0054] Figure 2 Schematic diagram of the complete rotor profile structure of a low gas torque rotor and a high gas torque rotor according to an embodiment of the present invention;

[0055] Figure 3 Schematic diagram of the rotor profile meshing process according to an embodiment of the present invention;

[0056] Figure 4 Schematic diagram of the rotor profile structure with different shape control parameters according to an embodiment of the present invention:

[0057] (a) Comparison of rack curve shapes with different shape control parameters;

[0058] (b) Schematic diagram of the meshing relationship of rotor profiles with different shapes;

[0059] Figure 5 Schematic diagram of the variable pitch screw rotor structure formed by the rotor profile according to an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be described in further detail below with reference to the accompanying drawings.

[0061] like Figure 1-2 As shown, the single-tooth twin-screw rotor with low transmission requirements in the embodiment of the present invention, the rack curve A r B r C r D r E r From the straight line segment A r B r , Bezier curve segment B r C r , Bezier curve segment C r D r With straight line segment D r E r The rack curve A is solved by the meshing relationship. r B r C r D r E r The corresponding combined curve segment A1B1C1D1E1 of the low gas torque rotor profile and the combined curve segment A2B2C2D2E2 of the high gas torque rotor profile are respectively connected, and then the complete rotor profile structure of the low gas torque rotor and the high gas torque rotor is obtained by connecting the point-meshing cycloid segment E1A1 and the point-meshing cycloid segment E2A2.

[0062] like Figure 3 , Figure 4 Figures (a) and (b) in , and Figure 5 As shown in the figure, the complete rotor profile structure of the low gas torque rotor and the high gas torque rotor can reasonably complete the meshing motion. At the same time, by adjusting the design parameters, the rotor profile shape can be flexibly adjusted, and then the equal / variable pitch rotor structure can be constructed to realize the flexible adjustment of the gas resistance torque.

[0063] Figure 1 Generate the rack curve A of the twin-screw rotor profile r B r C r D r E r Middle curve segment A r B r is a straight line segment, and its length parameter can be set to γ1. r x r y r A r B r The parametric equation of the segment is:

[0064]

[0065] Where x AB with y AB Represents the straight line segment A r B r The horizontal and vertical coordinates of the rack curve A are shown in Figure 2. r B r C r D r E r The parameter, R p is the pitch circle radius, R p equal R1 and R2 represent the set root circle radius and tip circle radius respectively, γ1 is point B r Position setting parameters.

[0066] Bezier curve segment B r C r The position vector expression of the upper point is:

[0067]

[0068] Where r BC Represents the position vector of the point on the Bezier curve segment BC, r B With r C Represents point B r and point C r The position vector, r P1,AB With r P2,AB Represents point P respectively 1,AB and point P 2,AB The position vector of

[0069] Click P 1,AB and point P 2,AB Select line segment B r P 0,AB With line segment C r P 0,AB For a point on , the direction vector expression is:

[0070]

[0071] Where i 1,AB with i 2,AB Point P 1,AB and point P 2,AB The location parameter is the design parameter, r P0 Represents point P 0,AB Position vector of point P 0,AB For straight line B r P 0,AB With straight line C r P 0,AB The intersection of straight line B r P 0,AB With Oyr Axis parallel, straight line C r P 0,AB Passing point C r , point C r Via Oy r Axis, the slope is from point C r Determined by the direction vector at point C r The direction vector at is determined by the design angle β.

[0072] Point C r The position vector is:

[0073] r C =[0 δR p ]

[0074] Where δ is point C r The control variable is the design value.

[0075] Point B r The position vector is:

[0076] r B =[R p -R2 πR p -γR p ]

[0077] Bezier curve segment C r D r The position vector expression of the upper point is:

[0078]

[0079] Where r CD Represents Bezier curve segment C r D r The position vector of the upper point, r C With r D Represents point C r and point D r The position vector, r P1,CD With r P2,CD Represents point P respectively 1,CD and point P 2,CD The position vector of

[0080] Click P 1,CD and point P 2,CD Select line segment C respectively r P 0,CD With line segment D r P 0,CD For a point on , the direction vector expression is:

[0081]

[0082] Where i 1,CD with i 2,CD Point P 1,CD and point P 2,CD The location parameter is the design parameter, r P0,CD Represents point P 0,CD Position vector of point P 0,CD is the straight line C r P 0,CD With straight line D r P 0,CD The intersection of the straight line D r P 0,CD With Oy r Axis parallel, straight line C r P 0,CD With straight line C r P 0,AB parallel.

[0083] Point D r The position vector is:

[0084] r D =[R2-R p γ2R p ]

[0085] Where γ2 is point D r The control variable is the design value.

[0086] Straight line segment D r E r Point E r The position vector is:

[0087] r E =[R2-R p -πR p ]

[0088] like Figure 2 As shown, in the rectangular coordinate system O1x1y1, the profile expression of the combined curve segment A1B1C1D1E1 is as follows:

[0089]

[0090] In the rectangular coordinate system O2x2y2, the profile expression of the combined curve segment A2B2C2D2E2 is as follows:

[0091]

[0092] Where r A1B1C1D1E1 Represents the position vector of a point on the combined curve segment A1B1C1D1E1 in the rectangular coordinate system O1x1y1, r A2B2C2D2E2Represents the position vector of a point on the combined curve segment A2B2C2D2E2 in the rectangular coordinate system O2x2y2, r AE with y r AE Respectively expressed in coordinate system Ox r y r Middle rack curve A r B r C r D r E r The horizontal and vertical coordinate vectors of the upper point, t represents the rack curve A r B r C r D r E r The parameter variable, φ represents the intermediate angle variable parameter, and the relationship between φ and t is:

[0093]

[0094] exist Figure 2 In the equation, the profile expressions of the point meshing cycloid segment E1A1 and the point meshing cycloid segment E2A2 are:

[0095]

[0096] Where x AE with y AE They respectively represent the coordinate vectors of the midpoint meshing cycloid segment E1A1 of the coordinate system O1x1y1 or the midpoint meshing cycloid segment E2A2 of the coordinate system O2x2y2.

[0097] exist Figure 2 In the above, the rotor profile with low gas torque is obtained by connecting the combined curve segment A1B1C1D1E1 with the point meshing cycloid segment E1A1, and the rotor profile with high gas torque is obtained by connecting the combined curve segment A2B2C2D2E2 with the point meshing cycloid segment E2A2. The design parameters in the above profile generation process include: point B r Position setting parameters point γ1, point D r The control variable γ1, point C r The control variable δ, point C r The direction vector at determines the angle β, and the Bezier curve segment B r C r The shape control parameter i 1,AB with i 2,AB , Bezier curve segment C r D r The shape control parameter i 1,CD with i 2,CD .

[0098] like Figure 3 As shown, the rotor profile with low gas torque and the rotor profile with high gas torque can achieve correct meshing, such as Figure 4 As shown in Figures (a) and (b), by adjusting the design parameters of the above-mentioned profile generation process, the rotor profile shape can be flexibly adjusted. Figure 5 As shown, the above-mentioned profile can be used to form a constant pitch or variable pitch screw rotor structure.

[0099] The method for designing the profile of a single-tooth twin-screw rotor with low transmission requirements according to an embodiment of the present invention comprises the following steps:

[0100] The rotor tooth root circle radius R1 and tooth tip circle radius R2 are set according to the exhaust volume requirement;

[0101] Set point B according to sealing requirements r Position setting parameter γ1, control point D r The setting parameter γ2 of the position;

[0102] Design point C according to the rotor gas torque adjustment requirement r The control variable δ of the position;

[0103] Based on point C r The direction vector at determines the design angle β and sets the Bezier curve segment B r C r The shape control parameter i 1,AB with i 2,AB , set Bezier curve segment C r D r The shape control parameter i 1,CD with i 2,CD ;

[0104] Based on the above parameter design, generate the rack curve A r B r C r D r E r ::

[0105] In coordinate system O r x r y r In the middle, straight line segment A r B r The parametric equations are as follows:

[0106]

[0107] Where x AB with y AB Represents the straight line segment A r B r The horizontal and vertical coordinates of the rack curve A are shown in Figure 2.r B r C r D r E r The parameter, R p is the pitch circle radius, R p equal R1 and R2 represent the set root circle radius and tooth tip circle radius respectively, γ1 is point B r Position setting parameters.

[0108] In coordinate system O r x r y r In the figure, Bezier curve segment B r C r The position vector expression of the upper point is:

[0109]

[0110] Where r BC Represents the position vector of the point on the Bezier curve segment BC, r B With r C Represents point B r and point C r The position vector, r P1,AB With r P2,AB Represents point P respectively 1,AB and point P 2,AB The position vector of

[0111] Click P 1,AB and point P 2,AB Select line segment B r P 0,AB With line segment C r P 0,AB For a point on , the direction vector expression is:

[0112]

[0113] Where i 1,AB with i 2,AB Point P 1,AB and point P 2,AB The location parameter is the design parameter, r P0 Represents point P 0,AB Position vector of point P 0,AB Line B r P 0,AB With straight line C r P 0,AB The intersection of straight line B r P 0,AB With Oy r Axis parallel, straight line C r P0,AB Passing point C r , point C r Via Oy r Axis, the slope is from point C r Determined by the direction vector at point C r The direction vector at is determined by the design angle β.

[0114] Point C r The position vector is:

[0115] r C =[0 δR p ]

[0116] Where δ is point C r The control variable is the design value;

[0117] Point B r The position vector is:

[0118] r B =[R p -R2 πR p -γR p ]

[0119] Bezier curve segment C r D r The position vector expression of the upper point is:

[0120]

[0121] Where r CD Represents Bezier curve segment C r D r The position vector of the upper point, r C With r D Represents point C r and point D r The position vector, r P1,CD With r P2,CD Represents point P respectively 1,CD and point P 2,CD The position vector of

[0122] Click P 1,CD and point P 2,CD Select line segment C respectively r P 0,CD With line segment D r P 0,CD For a point on , the direction vector expression is:

[0123]

[0124] Where i 1,CD with i 2,CDPoint P 1,CD and point P 2,CD The location parameter is the design parameter, r P0,CD Represents point P 0,CD Position vector of point P 0,CD is the straight line C r P 0,CD With straight line D r P 0,CD The intersection of the straight line D r P 0,CD With Oy r Axis parallel, straight line C r P 0,CD With straight line C r P 0,AB parallel;

[0125] Point D r The position vector is:

[0126] r D =[R2-R p γ2R p ]

[0127] Where γ2 is point D r The control variable is the design value.

[0128] Straight line segment D r E r Point E r The position vector is:

[0129] r E =[R2-R p -πR p ]

[0130] According to the meshing theorem, the rack curve A can be defined r B r C r D r E r Calculate the combined curve segment A1B1C1D1E1 of the low gas torque rotor profile and the combined curve segment A2B2C2D2E2 of the high gas torque rotor profile. In the rectangular coordinate system O1x1y1, the combined curve segment A1B1C1D1E1 can be expressed as:

[0131]

[0132] In the rectangular coordinate system O2x2y2, the combined curve segment A2B2C2D2E2 can be expressed as:

[0133]

[0134] Where r A1B1C1D1E1Represents the position vector of a point on the combined curve segment A1B1C1D1E1 in the rectangular coordinate system O1x1y1, r A2B2C2D2E2 Represents the position vector of a point on the combined curve segment A2B2C2D2E2 in the rectangular coordinate system O2x2y2, r AE with y r AE Respectively expressed in coordinate system Ox r y r Middle rack curve A r B r C r D r E r The horizontal and vertical coordinate vectors of the upper point, t represents the rack curve A r B r C r D r E r The parameter variable, φ represents the intermediate angle variable parameter, and the relationship between φ and t is:

[0135]

[0136] The profile expressions of the point meshing cycloid segment E1A1 and the point meshing cycloid segment E2A2 are both:

[0137]

[0138] Where x AE with y AE They respectively represent the coordinate vectors of the midpoint meshing cycloid segment E1A1 of the coordinate system O1x1y1 or the midpoint meshing cycloid segment E2A2 of the coordinate system O2x2y2.

[0139] The combined curve segment A1B1C1D1E1 is connected with the point-meshing cycloid segment E1A1 to form a low gas torque rotor profile; the combined curve segment A2B2C2D2E2 is connected with the point-meshing cycloid segment E2A2 to form a high gas torque rotor profile.

[0140] The low gas torque rotor profile and high gas torque rotor profile formed by the above method can be used to generate a constant pitch or variable pitch screw rotor structure by lofting. The generated variable pitch screw rotor structure is as follows: Figure 5 shown.

[0141] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A single-tooth twin-screw rotor with low transmission requirements, characterized in that: The low gas torque rotor and the high gas torque rotor mesh with each other, wherein the profiles of the low gas torque rotor and the high gas torque rotor are formed by a rack curve. A r B r C r D r E r The generated combined curve segment is connected with the point meshing cycloid segment; the rack curve A r B r C r D r E r By straight line segment A r B r , Bezier curve segment B r C r , Bezier curve segment C r D r With straight line segment D r E r Connected composition, combined curve segment of low gas torque rotor profile A 1 B 1 C 1 D 1 E 1 and the combined curve segment of the high gas torque rotor profile A 2 B 2 C 2 D 2 E 2 and rack curve A r B r C r D r E r Satisfying the meshing relationship, the combined curve segment A 1 B 1 C 1 D 1 E 1 and combined curve segments A 2 B 2 C 2 D 2 E 2 Connect the points to mesh the cycloid segments E 1 A 1 Cycloid segment meshing with point E 2 A 2. Obtain the complete rotor profile structure of the low gas torque rotor and the high gas torque rotor; In the coordinate system O r x r y r In the above example, the straight line segment A r B r The parametric equations are as follows: Where, x AB and y AB Represents straight line segments A r B r The horizontal and vertical coordinates of t Represents a rack curve A r B r C r D r E r The parameter variables, R p is the pitch circle radius, R p equal , R 1 and R 2 respectively represent the set tooth root circle radius and tooth top circle radius, γ 1 is a point B r Setting parameters of position; The Bezier curve segment B r C r The position vector expression of the upper point is: Where r BC Represents a Bezier curve segment BC The position vector of the upper point, r B With r C Represent points B r with dot C r The position vector, r P1,AB With r P2,AB Represent points P 1,AB with dot P 2,AB The position vector of point P 1,AB with dot P 2,AB Select as line segments B r P 0,AB With line segment C r P 0,AB For a point on , the direction vector expression is: Where, i 1,AB and i 2,AB Points P 1,AB with dot P 2,AB The location parameter is the design parameter, r P0 Indicates a point P 0,AB The position vector of a point P 0,AB For a straight line B r P 0,AB With straight line C r P 0,AB The intersection of the straight line B r P 0,AB and Oy r Axis-parallel, straight line C r P 0,AB passing point C r ,point C r go through Oy r Axis, slope from point C r The direction vector at point C r The direction vector at is determined by the design angle β determined; point C r The position vector is: Where, δ for point C r The control variable is the design value; point B r The position vector is: 。 2. The single-tooth twin-screw rotor with low transmission requirements according to claim 1, characterized in that: The Bezier curve segment C r D r The position vector expression of the upper point is: Where r CD Represents a Bezier curve segment C r D r The position vector of the upper point, r C With r D Represent points C r with dot D r The position vector, r P1,CD With r P2,CD Represent points P 1,CD with dot P 2,CD The position vector of point P 1,CD with dot P 2,CD Select as line segments C r P 0,CD With line segment D r P 0,CD For a point on , the direction vector expression is: Where, i 1,CD and i 2,CD Points P 1,CD with dot P 2,CD The location parameter is the design parameter, r P0,CD Indicates a point P 0,CD The position vector of a point P 0,CD For a straight line C r P 0,CD With straight line D r P 0,CD The intersection of the straight line D r P 0,CD and Oy r Axis-parallel, straight line C r P 0,CD With straight line C r P 0,AB parallel; point D r The position vector is: Where, γ 2 is a point D r The control variable is the design value.

3. The single-tooth twin-screw rotor with low transmission requirements according to claim 2, characterized in that: The straight line segment D r E r On point E r The position vector is: 。 4. The single-tooth twin-screw rotor with low transmission requirements according to claim 3, characterized in that: In the rectangular coordinate system O 1 x 1 y 1, combined curve segment A 1 B 1 C 1 D 1 E The line expression of 1 is as follows: In the rectangular coordinate system O 2 x 2 y 2, combined curve segment A 2 B 2 C 2 D 2 E The line expression of 2 is as follows: Where r A1B1C1D1E1 Expressed in rectangular coordinate system O 1 x 1 y 1 combined curve segment A 1 B 1 C 1 D 1 E 1 is the position vector of the point, r A2B2C2D2E2 Expressed in rectangular coordinate system O 2 x 2 y 2 combined curve segments A 2 B 2 C 2 D 2 E 2 is the position vector of the point on, x r AE and y r AE Respectively expressed in the coordinate system Ox r y r Middle rack curve A r B r C r D r E r The horizontal and vertical coordinate vectors of the upper point, t Represents a rack curve A r B r C r D r E r The parameter variable, ϕ represents the intermediate angle variable parameter, ϕ and t The relationship is: 。 5. The single-tooth twin-screw rotor with low transmission requirements according to claim 3, characterized in that: The point meshes with the cycloid segment E 1 A 1 Cycloid segment meshing with point E 2 A The line expression of 2 is: Where, x AE and y AE Represents the coordinate system O 1 x 1 y 1 midpoint meshing cycloid segment E1A1 or coordinate system O 2 x 2 y 2 midpoint meshing cycloid segments E2A2 The coordinate vector of .

6. A method for designing a profile of a single-tooth twin-screw rotor with low transmission requirements as claimed in claim 3, characterized in that: The following steps are involved: Step 1: Design the rack curve A r B r C r D r E r : The rotor tooth root circle radius is set according to the exhaust volume requirement R 1 and the radius of the tooth tip circle R 2; Set points according to sealing requirements B r Position setting parameters γ 1. Control Point D r Position setting parameters γ 2; Adjust the design point according to the rotor gas torque demand C r Control variable of position δ ; Basis point C r The direction vector at determines the design angle β , set the Bezier curve segment B r C r Shape control parameters i 1,AB and i 2,AB , set the Bezier curve segment C r D r Shape control parameters i 1,CD and i 2,CD ; Step 2: According to the meshing theorem, the rack curve designed in step 1 A r B r C r D r E r Find the combined curve segment of the low gas torque rotor profile A 1 B 1 C 1 D 1 E 1 and the combined curve segment of the high gas torque rotor profile A 2 B 2 C 2 D 2 E 2; Step 3: Solve the point meshing cycloid segment E 1 A 1 Cycloid segment meshing with point E 2 A 2; Step 4: Combine the curve segments A 1 B 1 C 1 D 1 E 1 Cycloid segment meshing with point E 1 A 1 Connect to form a low gas torque rotor profile; combine the curve segments A 2 B 2 C 2 D 2 E 2 Cycloid segment meshing with point E 2 A 2 are connected to form a high gas torque rotor profile.

7. The profile design method according to claim 6, characterized in that: The low gas torque rotor profile and the high gas torque rotor profile are formed into a constant pitch or variable pitch screw rotor structure through lofting.

Images